Combine goat cheese, 2 tablespoons basil, and minced garlic; set aside.
Place each chicken breast half between 2 sheets of heavy-duty plastic wrap, and pound each half to a 1/4-inch thickness using a meat mallet or rolling pin. Divide the cheese mixture evenly among breast halves. Roll up jelly-roll fashion. Tuck in sides; secure each roll with wooden picks.
Heat the pasta sauce and whole garlic cloves in a large skillet over medium heat; add chicken. Cover and cook 25 minutes or until chicken is done. Serve over pasta. Garnish with 1 tablespoon basil.